Method and apparatus for removal of the double indication of defects in remote eddy current inspection of pipes

ABSTRACT

The apparatus employs the remote field eddy-current (RFEC) inspection technique to electromagnetically measure physical parameters of a metallic pipe. RFEC devices inserted into and displaced along a cylindrical pipes may be used to measure the ratio of pipe thickness to electromagnetic skin-depth and thus allow for the non-invasive detection of flaws or metal loss. Typically these RFEC thickness measurements exhibit a so-called double-indication of flaws, an undesired artifact due to a double-peaked geometrical sensitivity function of the device. 
     The method describes a means by which this double indication artifact may be removed by an appropriate processing of RFEC measurements performed by an apparatus specifically designed for this purpose. The invention is particularly well designed for applications in the oilfield industry.

This is a continuation application of co-pending U.S. patent applicationSer. No. 13/266,129 to Emmanuel Legendre, filed under national phase ofPCT/EP2010/003800 on Jun. 25, 2010 which claims priority of EP09290508.2filed on Jun. 30, 2009, and entitled “Method and Apparatus for Removalof The Double Indication of Defects in Remote Eddy Current Inspection ofPipes,” which is hereby incorporated in its entirety for all intents andpurposes by this reference.

BACKGROUND

This application relates to a method and apparatus for detectingcorrosion loss in well bore tubulars; more specifically, this method andapparatus relate to the removal of double indication of defects fromvarying tubular geometries while performing remote field eddy currentnon-destructive inspection of such tubulars.

INTRODUCTION AND PRIOR ART

The inspection tool can be a mechanical caliper, an ultrasonic tool oran electromagnetic tool. The mechanical caliper comprises a plurality offingers for sensing the inner geometry of the casing. The mechanicalcalipers cannot be used for the determination of casing thickness,cannot distinguish non-metallic deposits on the casing from the metalliccasing itself, and may initiate corrosion by scratching the casingsurface. The ultrasonic tool measures the time-of-flight of asound-pulse between emission by the tool, reflections at the inner andouter surfaces of the casing and reception by the sound-wave detectorsin the tool. They may measure the inside diameter as well as thethickness of the casing. The ultrasonic tool cannot be used when thecasing transports a fluid mixture comprising a certain quantity of gasrelatively to liquid, and provides deteriorated reflected signals in thepresence of surface roughness that typically arise in corroded casing.

The electromagnetic tool is a non-destructive inspection tool. It may bebased either on the flux-leakage principle, the eddy-current principleor a combination thereof. The electromagnetic tool is insensitive tonon-conductive deposits and can operate irrespective of the nature ofthe fluid mixture flowing into the casing.

The electromagnetic tool based on flux-leakage principle is typicallyused for the detection of localized damage in ferromagnetic pipes. Thistool commonly subjects the casing to a strong static magnetic field. Dueto the ferromagnetic nature of the casing, the magnetic return flux ismainly confined to the inside of the metal casing. In the presence ofdiscontinuities in the metal, such as pits and holes caused bycorrosion, the magnetic flux “leaks” out of the body of the metal andmay be detected with appropriate magnetic sensors such as coils, Hallprobes, or magneto-resistive sensors. See, U.S. Pat. No. 6,924,640 toFickert et al. issued Aug. 2, 2005 for deployment of Hall-effectsensors. To allow for sufficiently sensitive and quantitativemeasurements, the flux-leakage based tool requires strong magneticfields and good flux coupling into the inspected body. This impliesclose proximity of the magnetic field source to the inner casingsurface. For further description of this method, one might review U.S.Pat. No. 3,940,689 to Johnson, issued Feb. 24, 1976 describing aflux-leakage and eddy current sensing device, which patent isincorporated by reference herein to further describe the background ofthis invention. The combinations of casings and tubing used inhydrocarbon wells often exhibit varying pipe diameters that render therequirements of sufficiently strong and well-coupled magnetic fluxdifficult to maintain. Furthermore, magnetic flux-leakage tools are notsuitable for measurements of gradual thinning of pipes.

The electromagnetic tool based on eddy-current principle is well suitedfor the measurement of both, inside diameter and wall thickness offerromagnetic metallic casing. See, for example, the description of thethickness coils in U.S. Pat. No. 4,292,588 to Smith, issued Sep. 29,1981, describing eddy current measurement of well bore tubulars. Thistool excites an alternating current in a coil transmitter adapted forinducing eddy-currents in the surrounding conductive casing and measuresthe induced voltage in a separate receiver coil. Alternatively, the toolmay measure the impedance of the transmitter coil. The transimpedance isaffected by the casing magnetic permeability (μ), electricalconductivity (σ) and the inner diameter of the nearby casing. In thecase of electromagnetic tool where sufficiently low frequencies andlarge coil separations are used, measurement of the transimpedance isused to extract the ratio of wall thickness d of the casing to skindepth δ, the so-called electromagnetic thickness (EM thickness) d/δ.

SUMMARY OF INVENTION

This apparatus for measuring ferromagnetic tubular thickness uses remotefield eddy current sensing and is made up of a body connected on awireline for insertion in a well bore tubular having a transmitter coiland a plurality of symmetrically situated receiver device on opposingsides of the transmitter coil; a circuit for energizing the transmittercoil at a selectable frequency; a circuit for receiving a signal fromeach receiver device and for processing the signal to eliminate a doubleindication of flaws.

Each receiver device is preferably a coil centered on the longitudinalaxis of the apparatus. The apparatus provides the ability to the userallowing the frequency to be selectable between 8.75, 17.5, 35, and 70Hz, which has been identified as low enough to permit theelectromagnetic force to penetrate the downhole tubular or casing and isdesigned to operate when the electromagnetic thickness, i.e. the ratioof the tubular wall thickness to the skin depth of the material, isequal to or less than five (5). The receiver coils are spaced a distancewhich, when divided by the inner diameter of the tubular, is greaterthan or equal to 2.5. For most tubulars or casing used in the oilfields, this suggests a frequency range between 8.75 and 70 Hz and atransmitter/receiver spacing of no less than 25 inches.

The apparatus preferably provides a four symmetrically spaced receivercoils, each pair spaced on opposing sides of the transmitter coil adistance of L1=k1×dz and L2=k2×dz, where k1 and k2 have no commondivisor and dz is an incremental length along the longitudinal axis ofthe apparatus. The circuit for receiving a signal and for processing thesignal to eliminate a double indication of flaws can be a programmabledigital computer providing a central processor, providing a memory andconnections to a analog to digital convertor for digitizing the signalto discrete data for processing by the programmable digital computer.

The apparatus can also consist of receivers selected from the one of thefollowing: coils, Hall effect voltage detectors, and magnetoresistivesensors without departing from the spirit or intent of this disclosure.

Generally, this apparatus for measuring defects in a well bore pipeusing remote field eddy current measurement provides a transmitter coiland a plurality of receiver coils in spaced axial relationship from eachother; a circuit generating a transmitter current and sensing a receivervoltage at each of the plurality of receiver coils collecting aconvoluted signal proportional to the thickness of the pipe adjacenteach receiver coil; and, a data analysis circuit which deconvolutes eachsensed signal to remove ghost-image signals from such receiver signal.Preferably, the receiver coils are symmetrically located on opposingsides of the transmitting coil. A preferred arrangement for thisapparatus for measuring defects in a pipe using remote field eddycurrent measurement comprises a transmitter providing a selectable lowfrequency electromotive force; a pair of receiver coils spacedlongitudinally on a first side of the transmitter and a pair of receivercoils spaced longitudinally on a second side of the transmitter eachpair of coils symmetrically matched with the similarly situated receivercoil on the opposing side of the transmitter; a circuit for correlatingthe transmitter current and the receiver voltages, as the apparatus ismoved through the pipe; thereby permitting the circuit to measure phasedeviations of a transimpedance as the apparatus moves past the samepoint in the pipe allowing the duplicate image to be eliminated and theimpulses transmitted and received by the transmitter to be averagedlowering a signal to noise ratio for the measurement of receivervoltage.

The apparatus allows a method for removing ghost defects from a remotefield eddy current sensing device comprising generating from atransmitter an eddy current on a well bore tubular outer surface;detecting the eddy current signal with more than one remote receiver;generating an eddy current signal on a well bore tubular outer surfacefrom an incrementally different position; detecting the eddy currentwith the more than one remote receiver from the incrementally differentposition; determining a linear combination of eddy current signalsdetected by the more than one remote receiver to eliminate ghost defectsin such received signals.

Essentially, this method for removing ghost defects from a remote fieldeddy current sensing device providing a transmitting coil and aplurality of symmetrically placed receiving coils on a longitudinal axisof the device provides the steps of exciting the transmitting coil in awell bore tubular with a low frequency current to induce an eddy currentin the well bore tubular; sensing an induced electromotive force at theplurality of receiving coils in a spaced relation with the transmittingcoil at a first location; storing a sensed signal from each receivingcoil at the first location; repeatedly moving the transmitting coil inthe well bore tubular to a new discrete location and sensing the inducedelectromotive force at the plurality of receiving coils for eachmovement of the transmitting coil; saving each sensed signal from eachreceiving coil at the plurality of locations; and, manipulating thesaved signal from each sensed coil to eliminate the duplicate readings.This processing can be accomplished in real time or stored in the memoryand processed at a later time or compared with earlier runs in the samewell bore tubular to detect long-term degradation in the thickness ofthe tubular. The method preferably provides four equal coils placed onopposing sides of a transmitting coil and spaced a distance L from thetransmitting coil which is at least 2.5 times the inner diameter of thetubular to be measured and the electromagnetic thickness of the tubularto be measured is less than or equal to 5.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 schematically shows a typical onshore hydrocarbon well locationand an enlarged portion of a zone where measurements are performed by astandard wireline device or tool.

FIG. 2 is a cross section view of a casing schematically showing themeasuring arrangement of the invention.

FIG. 3 is a schematic view of a preferred embodiment of the presentinvention showing two sets of symmetrically spaced receiver coils oneither side of a transmitter coil.

FIG. 4 describes a composite schematic graph of response function (G) ofa TX-RX coil pair in a casing superimposed over a graph showing “ghostimages” in the transimpedance phase PLF observed on existing toolsattenuating phase responses in the presence of casing collars with eachcollar identified with a ghost image due to the two-peaked responsefunction.

FIG. 5 shows a composite schematic example of a spaced tool arrangement,the top panel showing the transmitter and the two receiver coils at oneposition, and after the tool is moved to the right by an increment dz,the coils are shifted to the positions shown in the bottom panel.

FIG. 6 is a schematic graphical representation of a combination ofimpulse responses for the tool example shown in FIG. 5 in order toeliminate the double-peaked response of a single transmitter-receiver(TX-RX) pair.

FIG. 7 is a schematic example of a symmetric tool arrangement with k1=5and k2=6 on both sides of the central transmitter.

FIG. 8 is an example of ghosting-image removal processing showing the“raw” response (in the top panel) calculated with five groove defects inthe casing wall (shown at bottom panel).

DETAILED DESCRIPTION OF AN EMBODIMENT OF THE INVENTION

FIG. 2 shows schematically the measuring arrangement 1 according to apreferred embodiment of the invention. The measuring arrangement 1 isfitted within the logging tool TL illustrated in FIG. 1.

In the preferred embodiment of the invention all measurements of thetool are based on the determination of the transimpedance Z which isdefined as the mutual impedance between the transmitter current I andthe receiver voltage V of a given transmitter-receiver pair:

$\begin{matrix}{Z = \frac{V}{I}} & {{Eq}.\mspace{14mu}(1)}\end{matrix}$The tool response may be compared to that of a poorly coupled and lossytransformer where the transmitter of the primary circuit induces avoltage in the receiver coil of the secondary circuit. This mutualinductance coupling is composed of flux-coupling through the mediuminside the casing and of contributions by flux passing through the metaland outside of the pipe. The electromagnetic field is strongly affectedby eddy-currents inside the metal, which flow circumferentiallyvirtually uninhibited. The magnetic field inside the casing has adominating axial component. Changes in the properties of the metal—suchas the thickness—manifest themselves in corresponding changes of thetransimpedance Z.

Preferably, an air-calibration is performed. The calibrated measurementratio M can be defined as:

$\begin{matrix}{M = {\frac{Z}{Z_{air}} = \frac{V/I}{V_{air}/I_{air}}}} & {{Eq}.\mspace{14mu}(2)}\end{matrix}$The calibrated measurement ratio M is advantageous because the ratio Mbecomes insensitive to biases due to the measuring arrangementrealization. The biases are typically caused by the number of turns inthe coils and effect of metallic parts, such as metallic sleeves and themeasuring arrangement body. However, the calibrated measurement ratio Mdoes not compensate for variations of the air or casing measurement dueto temperature, pressure, and drift in the electronic arrangement.

In general, we can decompose the transimpedance Z or the ratio M eitherinto a in-phase (real) component R and out-of-phase (imaginary)component R or into a real amplitude A and relative phase φ, forinstance

$\begin{matrix}{Z = {\frac{V}{I} = {{R + {iX}} = {A\;{{\exp\left( {i\;\varphi} \right)}.}}}}} & {{Eq}.\mspace{14mu}(3)}\end{matrix}$The measuring arrangement 100 is shown schematically in FIG. 2. The toolprovides a transmitter coil 110 and receiver coils 120 (only one ofwhich is shown in this drawing) situated on the longitudinal axis of thetool Ax. In the preferred embodiment of the invention all transmittersand receivers are solenoids with axes parallel or equal to the tool axisAx. As previously noted, receivers may alternatively be solid statedevices such as Hall-effect, magnetoresistive devices or other magneticfield sensors.

A transimpedance is determined for each pair defined by a given receivercoil and the single transmitter. As is well known by those havingordinary skill in this art, all coils are characterized by a coilgeometry, such as number of turns of the coils, length of coils, windingradii and wire gauges. Additionally, the relative position of a giventransmitter-receiver pair is determined by the mutual spacing L alongthe tool axis Ax.

Furthermore, a measurement is characterized by the operating frequency,which may be a multitude of user-selectable frequencies. The measurementarrangement is designed specifically to optimize the sensitivity of thetransimpedance measurement to the desired physical parameter, which isthe average EM thickness of a given cross-section of the pipe.

It is convenient to use dimensionless variables to classify the responseof the pipe to the various sensor geometries and frequencies. We alreadymentioned the pipe EM thickness is the ratio d/δ where d is the pipethickness d=′−a (see FIG. 2), the skin depth 6 is given by

$\begin{matrix}{{\delta = \sqrt{\frac{2}{\sigma\;\mu\;\omega}}},} & {{Eq}.\mspace{14mu}(4)}\end{matrix}$with the casing magnetic permeability μ and electrical conductivity σfor a transmitter angular frequency of ω=2πf. A second dimensionlessquantity L/(2a) describes the sensor spacing relative to the pipediameter.Remote Field Eddy Current Regime

For small ratio

$\begin{matrix}{\frac{d}{\delta} \leq 5} & {{Eq}.\mspace{14mu}(5)}\end{matrix}$—the large skin-depth limit—the electromagnetic fields can penetrate thepipe wall thickness and radiate into the region outside the casing(medium 3)—considered to be homogenous. This requires sufficiently lowexcitation frequencies (see below).

If additionally the spacing L between transmitter coil TC1 and receivercoil RC1 is sufficiently large, approximately given byL/(2a)≧2.5,  Eq. (6)the phase φ of the transimpedance measurement becomes nearly a linearfunction of the pipe EM thickness, given approximately by

$\begin{matrix}{\varphi = {{2\frac{d}{\delta}} = {2\; d{\sqrt{\frac{\sigma\;\mu\;\omega}{2}}.}}}} & {{Eq}.\mspace{14mu}(7)}\end{matrix}$

This is the so-called remote-field eddy-current (RFEC) regime. In thisregime, the direct waveguide-beyond-cutoff-like coupling betweentransmitter and receiver inside the pipe is sufficiently attenuated thatthe transimpedance response becomes dominated by the field which haspenetrated the pipe into the external medium 3 near the transmitter(picking up one phase shift of d/δ), propagated nearlydipole-radiation-like within medium 3 and finally re-entered across thepipe into medium 1 near the receiver (picking up a second phase shift ofd/δ). Measurements by the tool of phase φ are thus used to invert forthe EM thickness of the pipe. The upper limit of L/(2a) is a function ofthe signal-to-noise ratio (SNR) of the measurement. The voltage signalat the receiver is proportional to a complex propagation factor exp(ik 2d), where k=(1−i)/δ and where 2d is the double path through the casing.More generally written as

$\begin{matrix}{Z = {\frac{\exp\left( {{- 2}\; k\; d} \right)}{L^{3}}{f\left( {{d/\delta},{ID},{\mu/\sigma},L,b_{1},b_{2}} \right)}}} & {{Eq}.\mspace{14mu}(8)}\end{matrix}$where the dominating exponential has been separated, the remainingparameters in function ƒ( ) depend on the geometry of the tool and thecasing properties. The parameters b₁ 130 and b₂ 140 are the meantransmitter and receiver radii, ID (=2a in FIG. 2) is the inner diameterof the casing, μ/σ is the ratio of magnetic permeability to conductivityof the casing—the so-called electromagnetic properties of the casing.Inspection of Eq. (8) indicates that both amplitude and phase arecharacterized by the same quantity 2d/δ.

Even if multiple casings are present, the measurements obtained by thisapparatus still provide the total EM thickness, including thecontributions from outer metal pipes, as long as the field penetratingall layers can be detected with a sufficient SNR. Comparisons betweenlogs run at different times (“time-lapse”) can thus provide informationon gradual metal loss of the combined pipes. This method has long beenused in single strings corrosion detection systems.

Design Summary

The typical dimensionless parameters d/δ and L/(2a) required forsatisfactory tool measurements are between 0.2 and 5, and ≧2.5,respectively, for typical oil field tubulars. For the pipe'selectromagnetic parameters conductivity a and relative magneticpermeability

$\frac{\mu}{\mu_{0}}$fall in the ranges

$\begin{matrix}{{{3.9\frac{MS}{m}} \leq \sigma \leq {7.4\frac{MS}{m}}},} & {{Eq}.\mspace{14mu}(9)} \\{20 \leq \frac{\mu}{\mu_{0}} \leq 200} & {{Eq}.\mspace{14mu}(10)}\end{matrix}$where μ₀ is the vacuum permeability, while the geometrical parameters oftypical casings have ranges0.2 inch≦d≦0.9 inch and  Eq. (11)2.4 inch≦ID≦9 inch.  Eq. (12)A preferred embodiment utilizing the previous parameters suggest thefollowing frequency and transmitter-receiver-spacing ranges:

8.75 Hz≦f≦70 Hz and

25 inch≦L

The final choice of frequencies, spacings, coil lengths turns, coilturns and winding radii need to be determined based on optimizing thesensitivity of the transimpedance measurement to the desired pipeparameters and based on the requirements of data processing algorithms,all well known to those in this art. In particular there may be multiplereceivers at different spacings.

The preferred embodiment of the present invention provides a userselectable frequency f of 8.75, 17.5, 35 and 70 Hz, with a receiver coilspacing on each side of the transmitter coil of L=[−36, −30, +30, +36]inches, with the origin of the z or longitudinal axis shown in FIG. 3 atthe transmitter coil.

Note that in this embodiment, receiver coil measurements are done at onefrequency selected from a choice of four. Note also, that we haveindicated four spacings L associated with the RFEC average EM thicknessmeasurement.

The choice of four receivers, symmetrically spaced above and below thetransmitter 300, is illustrated in FIG. 3. They are called Double CoilsA (310 at spacing L_(A1)=−36″ and 320 at spacing L_(A2)=−30″) and DoubleCoils B (330 at spacing L_(B1)=30″ and 340 at spacing L_(B2)=36″). Thechoice for this arrangement allows for the removal of double indicationof flaws, the so-called “ghost image” removal, of the RFEC average EMthickness measurements as described below.

The transmitter 300 operates at one of a selection of frequencies suchas, 8.75 Hz, 17.5 Hz, 35 Hz, 70 Hz to ensure an operator can optimizethe signal-to-noise ratio (SNR) and thickness resolution for a givencondition at a well site. While 35 Hz would typically allow the tool towork in a single casing, it may be required to measure at lowerfrequencies in order to log thick casings or multi-casings.

The following TABLE A summarizes coil specifications and typical signallevels of transmitter currents and receiver voltages for this embodimentof the apparatus described herein.

TABLE A Number Mean DC re- rms Signal Transmitter of Length radiussistance Level Coil coils [inch] [inch] Turns [Ohm] [A] 300 1 14 0.767550 61 0.5 @ 35 Hz Number Mean DC re- rms Signal of Length radiussistance Level Receiver Coils coils [inch] [inch] Turns [Ohm] [V] 310,320, 4 3 0.56 9275 7035 1e−3 @ 330, 340 35 HzMean coil radius is the average value of inner and outer coil diameter.All values at 20° C.

Having defined the operational ranges and design parameters of allsensors, we discuss the processing concepts below.

Removal of Double Indication of Flaws

As the apparatus moves through step-like changes of EM-thickness such aspassing through casing collars, instead of observing one phase deviationof a given transimpedance due to the local increase of metal, thevariation is present two times, once the transmitter is approaching thecollar, and a second time when the receiver is viewing the same collar(see FIG. 4). This is due to the geometrical factor that is concentratedwithin the casing radially and located around the transmitter andreceiver in the z-direction. This undesired ghost-image artifact hindersthe interpretation of EM thickness measurements in such tools.

The phase shift (σ) of the transimpedance responds to variations of EMthickness like a convolution up to first order:σ(z)=∫dy·(h _(T)(y−z _(T))+h _(R)(y−z _(R)))·th(y)  Eq. (13)where th(y) is the thickness (function of depth y), h_(R) and h_(T) arethe responses of the receiver coil and transmitter coil with positionsz_(R) and z_(T), respectively. This approximation assumes there areneither major contributions from the casing electromagnetic properties,nor strong variations of the casing inner diameter in the region ofinterest.

Different designs for the transmitter coils and receiver coils areuseful. Therefore, the functions h_(R) and h_(T) will be different.Accordingly, receivers located on each side of the transmitter arepreferably equivalent receivers, symmetrically placed. As shown in FIG.3, therefore, coil 310 will be equivalent to coil 340, and coil 320 willbe equivalent to coil 330. In the present embodiment, each of thesecoils is identical. With such a tool configuration, at each toolposition, the phase shift measured between transmitter and the firstreceiver could be compared with phase shift measured between transmitterand second receiver when the tool is translated to the position wheretransmitter lies on previous position of the first receiver and thesecond receiver lies at the previous position of the transmitter. Inparticular, the average of these two phase-shifts will follow thefollowing equation:

${\frac{1}{2}\left( {{\varphi_{1}(z)} + {\varphi_{2}(z)}} \right)} = {\frac{1}{2}{\int{{\mathbb{d}y} \cdot \left\{ {\left( {{h_{T}\left( {y - z_{T}} \right)} + {h_{R\; 1}\left( {y - z_{T}} \right)}} \right) + \left( {{h_{T}\left( {y - z_{R}} \right)} + {h_{R\; 2}\left( {y - z_{R}} \right)}} \right)} \right\} \cdot {{th}(y)}}}}$So if a receiver's impulse responses could be approximated as beingequal, the impulse response can be approximated as:

$\begin{matrix}{g = {{{\overset{\sim}{h}\left( {y - z_{T}} \right)} + {\overset{\sim}{h}\left( {y - z_{R}} \right)}} = {\overset{\sim}{h} \otimes \frac{{\delta\left( {y - z_{T}} \right)} + {\delta\left( {y - z_{R}} \right)}}{2}}}} & {{Eq}.\mspace{14mu}(14)}\end{matrix}$

This combined impulse response {tilde over (h)} contains contributionsof h_(R) and h_(T). Furthermore, last equation is formally equivalent ofsaying that measured phase shift is the convolution of two Dirac deltaswith metal thickness convoluted with {tilde over (h)}. And we canconclude that taking the average of phase shifts with appropriate tooltranslation is a way to handle un-symmetry between transmitter andreceivers impulse functions. In this specification, each coils impulseresponse will be considered equal.

The ghost image removal algorithm is designed to use severalreceiver-transmitter (RX-TX) spacings to deconvolve σ using data atdifferent spacings and at different “measurement times” i.e. toolpositions. The objective is to remove the two delta functions inequation (14) and to replace them with a single function. This allowsthe apparatus to determine the exact position of each imperfection inthe casing.

Consider first a solution proposed for two spacings, L1 and L2. Supposethat:L1=k1×dz  Eq. (15)L2=k2×dz  Eq. (16)where dz is a multiple of the vertical sampling and (k1, k2) areintegers with no common divisors. Let us sample the response function atthe same sampling interval dz. For the spacing L1, we have for instance:φ(z _(i))=α_(T)(z _(i))+α_(R)(z _(i) +L1)=α_(T)(i)+α_(R)(i+k1)  Eq. (17)The problem expresses itself as a linear system linking observations (φ)with the convolution of thickness with impulse responses of thetransmitter and receiver (α_(T) and α_(R)).

As an example, we may consider the case k1=1 and k2=2. The correspondingtool arrangement is shown schematically in FIG. 5. FIG. 6 is a schematicrepresentation of a combination of impulse responses for the toolexample with k1=1 and k2=2 as shown in FIG. 5 in order to eliminate thedouble-peaked response of a single TX-RX pair. The top (a) shows theresponse associated with the transmitter and a receiver coil at spacingL1=dz at one log position. After the tool moved to the right by anincrement dz the response of the same TX-RX pair in the shifted positionis shown in the middle (b). The third line of the graph shows theresponse associated with the transmitter and a receiver coil at spacingL2=2dz at the initial log position. Finally, the bottom graph (d) is thelinear combination of the responses (a)−(b)+(c), which exhibits only asingle peak, i.e. no ghost-image response.

One of the solutions to the problem of removing the double indication offlaws is shown in FIG. 6. In this case a linear combination of tworesponses of the short-spacing coil pair (L1=dz) at different samplingpositions 0 and +dz and of the response of the long-spacing coil pair(L2=2dz) provides the desired result. The three ways of forming asingle-peak response can be represented byf ₁ =g(0,L1)−g(dz,L1)+g(0,L2)f ₂ =g(0,L1)+g(dz,L1)−g(0,L2)f ₃ =−g(0,L1)+g(dz,L1)+g(0,L2)  Eq. (17)A simple way to obtain the solutions is to create the matrix S

$\begin{matrix}{S = \begin{pmatrix}{.5} & {.5} & 0 \\0 & {.5} & {.5} \\{.5} & 0 & {.5}\end{pmatrix}} & {{Eq}.\mspace{14mu}(18)}\end{matrix}$corresponding to the response function linked to the delta functions ofeq. 14 where each column represents a position in units of the samplinginterval dz. The first two rows correspond to the short-spacing coilpair (L1=dz) at different sampling positions 0 and +dz and the third rowcorresponds to the response of the long-spacing coil pair (L2=2dz) atposition 0.Inspecting the inverse of the matrix S

$\begin{matrix}{{(S)^{- 1} = \begin{pmatrix}1 & {- 1} & 1 \\1 & 1 & {- 1} \\{- 1} & 1 & 1\end{pmatrix}}\;} & {{Eq}.\mspace{14mu}(19)}\end{matrix}$one can identify the coefficients of the solutions given by equationseqs. (17). In general, if several measurements with the fixed coilspacings and with some depth shifting (multiples of dz) are considered,a system of equations can be created and solved using techniques wellknown in this art.

To adapt the ghost-removal processing to the requirements of RFEC toolsregarding minimal spacing L/(2a) 2.5, maximal spacing limited by SNR,sampling interval or other constraints it is possible to find other toolarrangements characterized by (k1, k2).

Another particular embodiment of the invention which satisfies all theabove conditions may be k1=5 and k2=6, where dz=6 inches. In this casematrix S and its inverse take the form

$\begin{matrix}{{S = \begin{pmatrix}{.5} & 0 & 0 & 0 & 0 & {.5} & 0 & 0 & 0 & 0 & 0 \\0 & {.5} & 0 & 0 & 0 & 0 & {.5} & 0 & 0 & 0 & 0 \\0 & 0 & {.5} & 0 & 0 & 0 & 0 & {.5} & 0 & 0 & 0 \\0 & 0 & 0 & {.5} & 0 & 0 & 0 & 0 & {.5} & 0 & 0 \\0 & 0 & 0 & 0 & {.5} & 0 & 0 & 0 & 0 & {.5} & 0 \\0 & 0 & 0 & 0 & 0 & {.5} & 0 & 0 & 0 & 0 & {.5} \\{.5} & 0 & 0 & 0 & 0 & 0 & {.5} & 0 & 0 & 0 & 0 \\0 & {.5} & 0 & 0 & 0 & 0 & 0 & {.5} & 0 & 0 & 0 \\0 & 0 & {.5} & 0 & 0 & 0 & 0 & 0 & {.5} & 0 & 0 \\0 & 0 & 0 & {.5} & 0 & 0 & 0 & 0 & 0 & {.5} & 0 \\0 & 0 & 0 & 0 & {.5} & 0 & 0 & 0 & 0 & 0 & {.5}\end{pmatrix}}\;} & (20) \\{{(S)^{- 1} = \begin{pmatrix}1 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 & 1 \\1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 \\1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 \\1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 \\1 & 1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 1 \\1 & 1 & 1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & 1 & 1 & 1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} & {- 1} \\{- 1} & {- 1} & 1 & 1 & 1 & 1 & 1 & 1 & {- 1} & {- 1} & {- 1} \\{- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 & 1 & 1 & {- 1} & {- 1} \\{- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 & 1 & 1 & {- 1} \\{- 1} & {- 1} & {- 1} & {- 1} & {- 1} & 1 & 1 & 1 & 1 & 1 & 1\end{pmatrix}}\;} & (21)\end{matrix}$

We find again that several solutions are possible, and among them, onlyone has the property of having the same weight applied on all shortspacings and all long spacings. The combination is simply the sum of allshort spacing measurements minus all long spacing measurements that arearound one depth with an interval of length (k1+k2)*dz. In the aboveexample, this specific solution is the 6-th row of coefficients(S)₆ ⁻¹=(1 1 1 1 1 1 −1 −1 −1 −1 −1)  (22)This processing scheme is an averaging of short spacing minus average oflong spacing, which explains why this scheme is robust to Gaussiannoise.

As explained previously, the tool is symmetrized by addition ofsymmetrically placed receivers, and de-ghosting algorithm is applied onsymmetrized phase shifts (taking the average phase shift when flippingTX and RX positions).

A preferred embodiment of this symmetrical tool arrangement, using onlytwo pairs of symmetric TX-RX spacings, is shown in FIG. 7. In this casek1=5 and k2=6, where dz=6 inches. It corresponds to the designparameters given above. An example of the processing results using thesolution of eq. (22) is shown in FIG. 8. One can generalize thealgorithm to larger number of spacing arrangements. Using spacings witha ratio of large integers increases in the noise amplification in theprocessing.

Numerous embodiments and alternatives thereof have been disclosed. Whilethe above disclosure includes the best mode belief in carrying out theinvention as contemplated by the named inventors, not all possiblealternatives have been disclosed. For that reason, the scope andlimitation of the present invention is not to be restricted to the abovedisclosure, but is instead to be defined and construed by the appendedclaims.

What is claimed is:
 1. An apparatus for measuring ferromagnetic tubularthickness using remote field eddy current sensing comprising: a toolbody suitable for insertion in a tubular, wherein the tool bodycomprises a transmitter coil and a plurality of receiver devices,wherein each receiver device of the plurality of receiver devices issituated on opposing sides of the transmitter coil, and wherein eachreceiver device is coil centered on a longitudinal axis of theapparatus; a circuit for energizing the transmitter coil at a selectablefrequency; and a circuit for receiving a signal from each receiverdevice.
 2. The apparatus of claim 1 wherein the circuit is suitable forprocessing the signal from each receiver device to eliminate a doubleindication of flaws.
 3. The apparatus of claim 1 wherein the circuit isa programmable digital computer providing a central processor, a memoryand connections to an analog to digital convertor for digitizing thesignal to discrete data for processing by the programmable digitalcomputer.
 4. The apparatus of claim 1 wherein the circuit is suitablefor correlating a current of the transmitter with the signal receivedfrom each receiver device, as the apparatus is moved through thetubular.
 5. The apparatus of claim 4 wherein the circuit is suitable formeasuring phase deviations of a transimpedance as the apparatus movespast a substantially same point in the tubular such that a duplicateimage is eliminated.
 6. The apparatus of claim 5 wherein the circuit issuitable for averaging impulses transmitted and received by thetransmitter coil to lower a signal to noise ratio for the signalmeasured from each receiver device.
 7. The apparatus of claim 1 whereinthe frequency is selectable between 8.75, 17.5, 35, and 70 Hz.
 8. Theapparatus of claim 1 wherein the receiver coils are spaced a distancewhich, when divided by the inner diameter of the tubular, is greaterthan or equal to 2.5.
 9. The apparatus of claim 1 wherein the pluralityof symmetrically spaced receiver coils is comprised of four coils, eachpair spaced on each side of the transmitter coil a distance of L1=k1×dzand L2=k2×dz, where k1 and k2 have no common divisor and dz is anincremental length along the longitudinal axis of the apparatus.
 10. Theapparatus of claim 1 wherein the receiver devices are selected from theone of the following: coils, Hall effect voltage detectors, andmagnetoresistive sensors.
 11. An apparatus for measuring defects in awell bore pipe using remote field eddy current measurement comprising: atransmitter coil and a plurality of receiver coils in spaced axialrelationship from each other, wherein each of the plurality of receivercoils are spaced a distance apart which, when divided by an innerdiameter of the well bore pipe, is greater than or equal to 2.5; acircuit suitable for: generating a transmitter current; sensing areceiver voltage at each receiver coil of the plurality of receivercoils; and collecting a convoluted signal proportional to a thickness ofthe pipe adjacent each receiver coil; and a data analysis circuit whichdeconvolves the convolved signal to remove ghost-image signals.
 12. Theapparatus of claim 7 wherein the receiver coils are symmetricallylocated on opposing sides of the transmitting coil.
 13. A method ofremoving ghost defects from a remote field eddy current sensing devicecomprising: generating from a transmitter an eddy current on a tubularouter surface at a first position; detecting the eddy current signalfrom the first position with more than one remote receiver; generatingan eddy current signal on a tubular outer surface at a second position;detecting the eddy current from the second position with the more thanone remote receiver; determining a linear combination of eddy currentsignals detected by the more than one remote receiver to eliminate ghostdefects in the eddy current signals.
 14. The method of claim 13,comprising exciting the transmitting with a low frequency current togenerate the eddy current in the tubular outer surface.
 15. The methodof claim 13, comprising storing the detected eddy current signal fromthe first position.
 16. The method of claim 15, comprising storing thedetected eddy current signal from the second position.
 17. The method ofclaim 13, comprising: repeatedly moving the transmitter in the tubularto a different position; generating an eddy current signal on a tubularouter surface at a different position; and detecting the eddy currentfrom the different position with the more than one remote receiver. 18.The method of claim 13 wherein the more than one remote receivercomprises four equal coils placed on opposing sides of a transmitter andspaced a distance L from the transmitter, wherein L is at least 2.5times an inner diameter of the tubular and wherein an electromagneticthickness of the tubular is less than or equal to 5.